Personally I think they're wonderful options (Montessori) and would love to be able to send my son to one. There are many flaws in schools that are yet to be extinguished and could have certain negative impacts on children, some more than others (one very silly example: my primary school acted as if we were naughty if we needed the toilet in lessons, and I got so embarrassed to ever need to go that I have a huge phobia of using someone else's bathroom resulting in a rather difficult week on an exchange trip to Spain

). I think Montessori schools do offer an advantage in that they are perhaps more sensitive to children's needs and ways of learning. Private schools are different. They have many of the flaws of public schools, except I think that the overall achievement is higher because of things like a higher budget, and the fact that parents sending their children to said schools are often from a wealthy and
sometimes more intellectual background, and so the children in general are predisposed to achieve; not to mention that things such as dyslexia would likely be diagnosed and supported much better in a private school. Also, if you're sending your child to a private school, you likely care about their education and so are actually involved with it and help out with homework and extra curricular activities etc which has a profound impact.
Going to a public school certainly isn't the end of the world though, and 90% of people here will be sending their children to one. There are many benefits of a public school, such as more integration with general society as opposed to only the very privileged, and there is often less focus on how much money you have (some private school kids I knew were obsessed with who had the best car/brands etc and at my school it was just normal if you were skint!). And anyway, many public schools (by public I mean state) are great, and if the parents get involved then they can become even better. Any benefits that a Montessori school could offer can no doubt be offered at home, too! Don't stress!
Sorry for the essay